Individual polymers at thermal equilibrium were exposed to an elongational flow producing a high strain rate; and their dynamics were recorded with video fluorescence microscopy. The flow was turned on suddenly so that the entire evolution of molecular conformation could be observed without initial perturbations. The rate of stretching of individual molecules is highly variable and depends on the molecular conformation that develops during stretching. This variability is due to a dependence of the dynamics on the initial, random equilibrium conformation of the polymer coil. The increasing appearance at high strain rates of slowly unraveling hairpin folds is an example of nonergodic dynamics, which can occur when a statistical mechanical system is subjected to nonadiabatic, or "sudden," external forces.